Radiotracer Residence Time Distribution Method for Industrial and Environmental Applications
Material for Education and On-the-Job Training for
Practitioners of Radiotracer Technology
TRAINING COURSE SERIES No. 31
Radiotracer Residence Time Distribution Method
for Industrial and
Environmental Applications
Material for Education and On-the-Job Training for Practitioners of Radiotracer Technology
INTERNATIONAL ATOMIC ENERGY AGENCY, VIENNA, 2008
The originating Section of this publication in the IAEA was:
Division for Asia and the Pacific International Atomic Energy Agency
Wagramer Strasse 5 P.O. Box 100 A-1400 Vienna, Austria
RADIOTRACER RESIDENCE TIME DISTRIBUTION METHOD FOR INDUSTRIAL AND ENVIRONMENTAL APPLICATIONS
IAEA-TCS-31 ISSN 1018–5518
© IAEA, 2008
Printed by the IAEA in Austria IAEA, VIENNA, 2008
FOREWORD
The International Atomic Energy Agency (IAEA) plays a major role in facilitating the transfer of the radiotracer technology to developing Member States. The major radiotracer techniques have been implemented through IAEA technical cooperation projects and adopted by many Member States.
The expertise and knowledge gained should be preserved. The sustainability of technology and knowledge preservation calls for creation of young specialists and for continuing good practices.
As a part of its involvement in human resource development, the IAEA is aware of the important need to prepare standard syllabi and training course materials for the education of specialists in different fields of nuclear technologies. This training course material is intended for the cultivation of radiotracer specialists and for continuing technical education of radiotracer practitioners worldwide.
The wide interest in radiotracer technology has created the need for high level professional education and training in this field, which are not necessarily covered by traditional university courses.
Radiotracers are playing more and more important roles in industry. These roles will continue to expand, especially if students and engineers are exposed in their academic training to the many possibilities for using this tool in research, development and applications. Besides educational purposes, this publication will assist developing Member States in establishing their quality control and accreditation systems.
This publication is based on lecture notes and practical works delivered by many experts in IAEA-supported activities. Lectures, papers, case studies and software were reviewed by a number of specialists in several meetings. In particular, S. Charlton, S.H. Jung, I.H. Khan, H.J. Pant and P. Zhang have provided substantial technical inputs. The IAEA wishes to thank all the specialists for their valuable contributions.
The IAEA officers responsible for this publication are P.M. Dias of the Department of Technical Cooperation, and Joon-Ha Jin of the Division of Physical and Chemical Sciences.
EDITORIAL NOTE
The use of particular designations of countries or territories does not imply any judgement by the publisher, the IAEA, as to the legal status of such countries or territories, of their authorities and institutions or of the delimitation of their boundaries.
The mention of names of specific companies or products (whether or not indicated as registered) does not imply any intention to infringe proprietary rights, nor should it be construed as an endorsement
CONTENTS
INTRODUCTION...1
1. ELEMENTS OF RADIATION PHYSICS ...2
1.1. Radiation and radioisotopes ...2
1.1.1. Structure of the atom...2
1.1.2. Alpha, beta and gamma...3
1.1.3. Neutrons ...6
1.1.4. Radioactive decay and half-life...6
1.2. Radiation units ...8
1.2.1. Unit of radioactivity ...7
1.2.2. Dose units...8
1.2.3. Radiation dose rate in the vicinity of a point source of gamma rays ...8
1.3. Radiation detection ...9
1.3.1. Gas filled radiation detectors ...9
1.3.2. Scintillation radiation detectors...10
1.3.3. Semiconductor (solid state) detectors ...10
1.3.4. Detector efficiency...11
1.4. Radiation protection and safety...12
1.4.1. ALARA principle...12
1.4.2. Radiation safety considerations in radiotracer applications...12
2. RADIOACTIVE TRACERS...13
2.1. Types of tracers...13
2.1.1. Intrinsic and extrinsic tracers ...14
2.2. Advantages of radiotracers...15
2.3. Selection of a radiotracer ...16
2.4. Methods and techniques for labelling ...17
2.4.1. Solid materials...17
2.4.2. Aqueous systems...20
2.4.3. Organic materials ...20
2.4.4. Gaseous materials ...21
2.5. Radionuclide generators for industrial applications...21
2.5.1. Major radionuclide generator-based radiotracers for industrial applications...21
2.5.2. Application of radionuclide generator-based radiotracers ...23
2.6. Mixing length estimation ...25
2.6.1. Definition of mixing length...25
2.6.2. Examples of injection techniques for reducing mixing length...26
3. RADIOTRACER DETECTION ...28
3.1. On-line and off-line measurements...28
3.2. On-line measurements using gamma radiotracers ...28
3.2.1. Influence ofd various parameters ...28
3.2.2. Data acquisition...31
3.3. Off-line measurements...33
3.3.1. Sampling measurement ...33
4. FORMULATION OF THE RESIDENCE TIME DISTRIBUTION ...35
4.1. Residence time distribution (RTD) measurement...35
4.2. RTD formulation...36
4.2.1. Dead time correction...37
4.2.2. Background correction...37
4.2.3. Radioactive decay correction ...37
4.2.4. Filtering (or smoothing) ...38
4.2.5. Data extrapolation ...39
4.2.6. Normalization of the area of experimental tracer curve...39
5. RTD TREATMENT AND MODELING...40
5.1. Calculation of moments ...40
5.2. RTD system analysis...41
5.2.1. Methodology ...41
5.2.2. Elementary models...42
5.2.3. Models for non-ideal flows ...43
5.2.4. Rules for combining simple models...47
5.2.5. Optimization procedure — Curve fitting method ...48
5.2.6. Example of simple modelling: Mixer cascade with three compartments ...49
5.3. Convolution and deconvolution procedures...51
5.3.1. Convolution...51
5.3.2. Deconvolution...53
6. PLANNING AND EXECUTION OF A RADIOTRACER EXPERIMENT ...53
6.1. Amount of activity ...53
6.1.1. Factors influencing the radiotracer activity...53
6.1.2. Estimation of radiotracer activity for RTD tests ...54
6.2. Implementation of the RTD test...55
7. RESIDENCE TIME DISTRIBUTION APPLICATIONS ...57
7.1. Major targets ...57
7.2. RTD for troubleshooting...58
7.2.1. Dead/stagnant volume...60
7.2.2. Bypassing/channelling ...60
7.3. RTD for diagnosis of industrial processes: Case studies ...61
7.3.1. Radiotracers for diagnosis of fluid catalytic cracking (F.C.C.) units...61
7.3.2. Liquid flow in trickle bed reactors ...64
7.3.3. RTD to solve the problem of fluid maldistribution within a packed bed tower...68
7.3.4. Radioatracer investigation of pulp flow dynamics in a phosphate chemical reactor ...71
7.3.5. Diagnosis of leaching and flotation processes ...75
7.3.6. Heavy metal release in a pilot plant scale municipal solid waste incinerator ...80
7.3.7. Gas flow distribution in a SO2 — Oxidation industrial reactor...83
7.3.8. Improvement of a grinding process...85
7.3.9. Investigation of cobalt recovery and mass flow dynamics in a copper melting process ...86
7.3.10. Estimation of laterite grain erosion in a fluidised bed calciner...88
7.3.11. Radiotracer valuation of coal-ash dust cyclone efficiency...89
7.3.12. RTD for diagnosing a concrete mixing machine ...90
7.3.13. Radiotracer for efficiency evaluation of irradiation chamber for flue gas treatment ...91
7.3.14. Radiotracer investigations of wastewater treatment plants ...94
7.3.15. Radiotracers for flow meter calibration ...109
7.3.16. Interwell tracer technique (IWTT) ...111
8. RTD SOFTWARE FOR MODELING SIMPLE FLOWS...117
8.1. A manual for the RTD software...117
8.1.1. Introduction: What does it do?...117
8.1.2. Data input — Preparing the calculation ...117
8.1.3. Running the calculation, seeing the results ...120
8.2. Description of models available in the RTD software ...123
8.2.1. Axial dispersed plug flow ...123
8.2.2. Axial dispersed plug flow with exchange ...123
8.2.3. Perfect mixers in series ...124
8.2.4. Perfect mixers in series with exchange ...124
8.2.6. Perfect mixers with recycle...125
8.3. Purpose of tutorials ...125
8.3.1. Tutorial to CASE 1 ...126
8.3.2. Tutorial to CASE 2 ...127
8.3.3. Tutorial to CASE 3 ...128
8.3.4. Tutorial to CASE 4 ...129
8.3.5. Case study exercise: Model of water flow by gravity through two tanks in series...131
9. LABORATORY WORKS ...133
9.1. Closed circuit water flow rig for laboratory RTD tests...133
9.1.1. Flow rig experimental setup...133
9.1.2. Some examples of radiotracer tests performed in the flow rig ...134
9.2. Laboratory Work 1: Determination and analysis of RTD in process vessels ...136
9.2.1. Theory ...136
9.2.2. Part A: Determination of the residence time distribution (RTD)...137
9.2.3. Part B: Parameter estimation by time-domain curve fitting...138
9.2.4. Part C: Parameter estimation by the method of moments...138
9.3. Laboratory Work 2: Detection of dead space and channelling ...139
9.3.1. Theory ...139
9.3.2. Part A: Detection of dead space...140
9.3.3. Part B: Detection of channelling (Bypassing)...141
9.4. Laboratory Work 3: RTD curves and parameter estimation in combined model systems...141
9.4.1. Theory ...141
9.4.2. Part A: Stirred tank in series with plug flow...143
9.4.3. Part B: Tanks in parallel...144
10. QUESTIONS ON RTD METHODOLOGY AND TECHNOLOGY ...144
BIBLIOGRAPHY ...149
CONTRIBUTORS TO DRAFTING AND REVIEW...153
INTRODUCTION
The concept of residence time distribution (RTD) has become an important tool for the analysis of industrial units and reactors. The RTD of fluid flow in process equipment determines their performance. Radiotracers are method of choice for obtaining the RTD in industrial processing vessels and wastewater treatment systems. Radiotracer RTD method has been extensively used in industry to optimize processes, solve problems, improve product quality, save energy and reduce pollution. The technical, economic and environmental benefits have been well demonstrated and recognized by the industrial and environmental sectors. Though the RTD technology is applicable across a broad industrial spectrum, the petroleum and petrochemical industries, mineral processing and wastewater treatment sectors are identified as the most appropriate target beneficiaries. These industries are widespread internationally and are of considerable economic and environmental importance.
There is little experience in teaching the use of radiotracers, and the available books on this subject are either application or principle oriented. This text is the result of the belief that there is a need to develop radiotracer RTD measurement applications from fundamental principles. The theoretical treatment is applied to the extent possible, but, when complete analytical treatments are not practical, a mechanistic or phenomenological approach is adopted. Although many applications are included as illustrations, this is not intended as a bibliography of applications. The application illustrations chosen represent the major problems of industry where the radiotracer RTD method is very competitive.
This training course material is organized into ten sections. The characteristics of nuclear radiation are described in section one on elements of radiation physics. Radiation and radioisotopes, radiation interactions, detection of radiation and detector responses are treated with emphasis on their projected use in the understanding and treatment of the radiotracer RTD methodology and applications that follow.
Radioactive tracers and radiotracer detection are covered in sections two and three, respectively.
Since radiotracer RTD is a general experimental technique with wide application, these two sections contain a discussion of the considerations that are generally useful in RTD applications. These considerations include a description of the tracer concept, general tracer requirement, special characteristics of radiotracers, their advantages, the selection and preparation of radiotracers, radiotracer detection systems, on-line and off-line detection modes in field and laboratory conditions.
Sections four and five describe the RTD formulation and modeling. Since its introduction into chemical engineering by Danckwerts in 1953 the concept of RTD has become an important tool for the analysis of industrial units. In spite of this “old age” it is still the subject of many publications in most important journals of chemical engineering concerning general or practical aspects of RTD. The concept of RTD is fundamental to reactor design. The experimental RTD is the base information for further treatment. Throughout its modeling it could be determined the optimal parameters for process simulation and control. The modeling is realized in general by mathematical equations involving empirical or fundamental parameters such as axial dispersion coefficients or arrangement of ideal mixers.
Section six provides some considerations about planning and execution of radiotracer experiments. Section seven deals with RTD applications for troubleshooting and diagnosing of typical industrial and environmental processes.
Section eight provides the insight of RTD software for modeling of simple flows. Tutorials demonstrate the application of the software to data sets from various tracer experiments. Each data set is analyzed with a particular model. The RTD software is user-friendly and can be employed for modeling of real industrial processes.
Section nine deals with laboratory work. The laboratory experiments are designed to illustrate radiotracer RTD measurement principles, and can be performed with simple, inexpensive, basic equipment, such as NaI detectors and data acquisition system; Tc-99m in low activity, easy to be found in nuclear medicine departments, is used as radiotracer . The flow rig designed for laboratory tests can easily be constructed in any tracer laboratories. Section ten provides questions for testing the knowledge’s of trainees.
1. ELEMENTS OF RADIATION PHYSICS
1.1. RADIATION AND RADIOISOTOPES
Radiation is defined as the emission of energy in the form of waves or particles through a medium. Examples include radio and TV waves, microwaves, radar, light (infrared, visible and ultraviolet), X rays and cosmic rays. The frequency of the waves determines the radiation characteristics.
Ionizing radiation has sufficient energy to interact with an atom and remove tightly bound electrons from their orbits, causing the atom to become charged or "ionized." Examples are alpha and beta particles, and gamma rays. Ionization provides the means for detecting radiation via special instruments (radiation detectors).
Radioactivity is a spontaneous process in which the unstable nucleus of an element "radiates"
excess energy in the form of particles (alpha, beta) or waves (gamma rays). This instability is caused by an excess of protons or neutrons. After this excess energy is released, either a lower energy atom of the same element or a new nucleus and element may be left. This process is referred to as a transformation, decay or disintegration of an atom.
1.1.1. Structure of the atom
In 1913, Danish physicist Niels Bohr proposed a model of the structure of the atom, based on quantum mechanics, henceforth referred to as the "Bohr atom”. It consisted of a central nucleus of protons and neutrons that are surrounded by orbiting electrons. Figure 1 shows the atom of helium.
FIG. 1. Bohr atom structure model for helium
The Bohr atom is not the most comprehensive or definitive model that exists of the atom but is suitable in explaining its basic structure. Atomic particle properties are as follows:
• Proton, net electrical charge +1 unit, rest mass 1.673 x 10-27 kg
• Neutron, net electrical charge 0, rest mass 1.675 x 10-27 kg
• Electron, net electrical charge –1 unit, rest mass 9.1066 x 10-31 kg.
Neutrons are only slightly more massive than protons; electrons are about 2000 times less massive than protons. The number of protons determines the element of the atom: hydrogen has one proton, helium has two protons, tungsten has 74 protons, uranium has 92 protons and so on.
The number of protons is known as the "atomic number" and is designated as "Z". Atoms with different numbers of protons are called "elements."
Atoms are normally electrically neutral: the total positive charge of protons equals the total negative charge of electrons. The sum of the protons and neutrons is known as the "atomic mass number," and is designated as "A." Neutrons make up the remaining mass of the nucleus and provide a mechanism to hold the protons in place. Without neutrons, the nucleus would split due to the repellent force between the positively charged protons.
Elements can have nuclei with different numbers of neutrons in them. Hydrogen, which usually only has one proton in the nucleus, can have a neutron added to its nucleus to form deuterium; two added neutrons would create tritium, the radioactive form of hydrogen. Atoms of the same element that vary in neutron number are called "isotopes". Some elements have many stable isotopes (tin has 10) while others have only one or two. Isotopes are depicted by "A" with the element abbreviation, e.g., 20Ne, where 20 represents "A" (sum of protons and neutrons) and Ne is the symbol for neon.
1.1.2. Alpha, Beta, and Gamma
British physicist Ernest Rutherford has discovered three kinds of radiation emitted by so-called radioactive materials, which he named after the first three letters of the Greek alphabet, alpha (α), beta (β) and gamma (γ). When Rutherford subjected a radioactive material to an electric field, he found out that the radiation was split in three beams (alpha, beta and gamma); alpha and beta were deflected towards opposite electric poles, while gamma not (Fig. 2).
FIG. 2. Alpha, beta and gamma under the effect of magnetic and electrical fields
Alpha particles
Alpha decay is a radioactive process in which a particle with two protons and two neutrons is ejected from the nucleus of a radioactive atom (Fig. 3). The alpha particle is similar to the nucleus of a helium atom. This decay occurs in very heavy elements such as uranium, thorium and radium. The nuclei of these atoms contain more neutrons than protons. Alpha particles have a charge of +2 units
due to the two protons and are relatively heavy and energetic compared to other radioactive emissions;
this causes alpha particles to interact readily with materials they encounter, including air, causing much ionization in a very short distance. This is referred to as a high linear energy transfer (LET).
Most alpha particles have energies between 4 and 6 MeV, will only travel a few centimeters in air and are usually stopped by a sheet of paper.
The observed half-lives are from microseconds to billions of years. This type of radiation poses an internal health hazard via inhalation, ingestion or absorption through the skin.
FIG. 3. Alpha decay Beta particles
There are two kinds of beta particles: beta minus (electron) and beta plus (positron). These particles derive from the process of a proton becoming a neutron or vice versa; if a neutron becomes a proton, a negatively charged electron is emitted; when a proton changes to a neutron a positively charged positron is emitted. Because electron and positron are emitted from the nucleus of the atom, they are called beta particle to distinguish them from the electrons that orbit the atom. A neutrino (or anti-neutrino) is also emitted during decay; it is a neutral particle that has almost no mass and carries away some of the energy from the decay process. Figure 4 shows the beta decay of K-40.
FIG. 4. Beta decay
Beta minus (or plus) particles have a single negative (or positive) charge and have a mass only a small fraction of a neutron or proton. As a result, beta particles interact less readily with material than alpha particles. Depending on the beta particle’s energy (which depends on the radioactive isotope), beta particles may travel up to several meters in air and are stopped by thin layers of metal or plastic.
Beta particles are only considered hazardous if they are ingested or inhaled.
After an alpha or beta decay reaction, the nucleus is often left in an "excited" state meaning that the decay has produced a nucleus that still has excess energy to get rid of. This energy is lost by
emitting a pulse of electromagnetic radiation called a gamma ray. The gamma ray is identical in nature to light or microwaves, but of very high energy.
Gamma radiation
Gamma rays are electromagnetic radiation emitted by radioactive decay; energies range from ten thousand to ten million electron volts. Like all forms of electromagnetic radiation, the gamma ray has no mass and no charge. Gamma rays interact with material by colliding with the electrons in the shells of atoms.
The three interactions are the photoelectric effect, Compton scattering and pair production. They lose their energy slowly in material, being able to travel significant distances before stopping.
Depending on their initial energy, gamma rays can travel up to hundreds of meters in air and can easily penetrate through most of the materials. Most alpha and beta emissions also include gamma rays as part of their decay process. Gamma emission accompanies normally the alpha and beta radiation;
there are no "pure" gamma emitters. Gamma radiation poses an external hazard.
Three processes are mainly responsible for the absorption of gamma rays (Fig.5):
• Photoelectric absorption,
• Compton scattering,
• Pair production (electron-positron).
FIG. 5. Principle of photoelectric absorption, Compton scattering and pair production
For a narrow beam of monoenergetic gamma rays of intensity I0 traveling through a medium of density ρ, the residual intensity after traversing a thickness x is given by:
I = I0exp( - μ.ρ.x) where: μ is the attenuation coefficient.
The above equation strictly applies only to narrow beams of radiation, and this is very difficult to guarantee in practice. For broad beams of radiation, the equation takes the form:
I = B I0 exp(- μpx)
where: B = "build-up" factor. This factor takes a practical detail into account namely the tendency of gamma rays to be scattered through any medium.
Penetration of matter
Though the most massive and most energetic of radioactive emissions, alpha particle is the shortest in range because of its strong interaction with matter. Gamma ray is extremely penetrating, and beta particles strongly interact with matter and have a rather short range (Fig. 6).
FIG. 6. Penetration of alpha, beta and gamma radiations into the matter
1.1.3. Neutrons
In 1920 scientists proposed the existence of a neutral (i.e., no charge) particle; in 1932, James Chadwick correctly interpreted the results of experiments conducted by French physicists Frederic and Irene Joliot-Curie and other scientists, and confirmed its existence. He named it the neutron. It is one of the elementary particles of which matter is formed.
The neutron is part of all atomic nuclei of mass number greater than 1; that is, all nuclei except ordinary hydrogen. Free neutrons - those outside of atomic nuclei - are produced in nuclear reactions.
Ejected from atomic nuclei at various speeds or energies, they are slowed down to very low energy by collisions with light nuclei, such as those of hydrogen, deuterium, or carbon. A free neutron is unstable and decays, forming a proton, an electron, and a neutrino. They are an external hazard best shielded by thick layers of concrete. Neutron irradiation of material causes the material to become radioactive (neutron activation) by changing the neutron to proton ratio in the nucleus.
Neutrons may collide with nuclei and undergo inelastic or elastic scattering. During inelastic scattering some of the kinetic energy that is transferred to the target nucleus excites the nucleus, and the excitation energy is emitted as a gamma photon. Elastic scattering is the most likely interaction between fast neutrons and low atomic-numbered absorbers. It can be shown that the energy E of the scattered neutron after a head-on elastic collision is:
E=Eo [(M-m)/(M+m)]2 where:
• Eo = energy of the incident neutron
• m = mass of the incident neutron
• M = mass of the scattering nucleus
From the formula, it is evident that light nuclides slow dawn fast neutrons very efficiently. For M= m the energy of the scattered neutrons is zero. Hydrogen is the most efficient for slowing down fast neutrons; this is the reason that water and paraffin are commonly used to thermalize fast neutrons.
1.1.4. Radioactive decay and half-life
Half-life (symbol: T½) is the time required for the quantity of a radioactive material to be reduced to one-half of its original value. After two half-lives, there will be one fourth the original sample, after three half-lives one eight the original sample, and so forth (Fig. 7). Practically, after 4-5 half-lives the radioisotope is almost disappeared. All radioisotopes have a particular half-life that ranges from fractions of a second to millions of years.
FIG. 7. Radioactive decay principle: half-life illustration
From radiation protection point of view, there are two kind of half-lives, one is the radiological or physical half-life (Tr) mentioned above, and the other is biological half-life (Tb), which is the time that biological organism reject the half of the radioisotope. The effective half-life Teff is the combination of both physical and biological half lives and is given by the following formula:
1/Teff = 1/Tr + 1/Tb Activity calculation after radioactive decay
Source activity at any time "t" is calculated from the activity at some original or zero time using the following formula:
A = Ao e-[0.693 x (t / T 1/2)]
Where:
• A= activity at time "t"
• Ao= activity at time zero
• t = time elapsed (same units as half-life)
• T1/2 = half-life
Example: What is the activity of 32P after 45 days, if the initial activity is 10000 Bq? Applying the half-life of 32P (14.3 days) in the formula above is results that the activity that remains after 45 days is:
A=10000 x e- 0.693 x 45 / 14.3 = 1129,5 Bq
1.2. RADIATION UNITS 1.2.1. Unit of radioactivity
Radioactive material is usually quantified by its activity rather than its mass. The activity is the number of disintegrations or transformations the quantity of material undergoes in a given period of time. The two most common units of activity are the Curie and the Becquerel (the SI unit.)
While working in Paris with several tons of uranium ore, Marie and Pierre Curie were able to separate two new elements which were even more radioactive than the uranium itself and named them as polonium and radium. It was found that 37 billion atoms disintegrate per second in 1 g of radium.
For the discovery of radium, the Curies were honored with the unit Curie, i.e. 1 Ci = 37 billion atoms disintegrating per second. This long-used unit of radioactivity has been replaced with the SI unit, the Becquerel (1 Bq = 1 disintegration per second). Henri Becquerel has discovered the phenomenon of radioactivity in 1896, in the course of his research on fluorescence. In 1903 he shared the Nobel Prize in physics with French physicists Marie Curie and Pierre Curie for work on radioactivity.
1 Ci = 3,7 x 1010 Bq
The Curie is a large amount of radioactivity while the Becquerel is a very small amount. For convenience, milli- (1 thousandth) and micro- (1 millionth) Curies or Mega- (million) and Giga (billion) Becquerel’s are used in everyday practice.
1.2.2. Dose units
Dose is a generic term that means absorbed dose, dose equivalent, effective dose equivalent, committed dose equivalent or total effective dose equivalent. Each of these is defined below:
Absorbed dose: It is the energy imparted by ionizing radiation per unit mass of irradiated material, and its measurement unit is the Gray (Gy). Gray is defined as a unit of energy absorbed from ionizing radiation, equal to 10 000 ergs per gram or 1 joule per kilogram of irradiated material. The unit Gray can be used for any type of radiation; it does not describe the biological effects of the different radiations. The old unit of absorbed dose is “rad”. New and old units are relation is: 1 Gray (Gy) = 100 rads.
Equivalent dose: This relates the absorbed dose in human tissue to the effective biological damage of the radiation. It is a multiplication of (absorbed dose) x (quality factor) x (other necessary modifying factors of interest). The Sievert (Sv) is a unit used to derive the "equivalent dose".
Normally, the equivalent dose is expressed in milliSieverts (mSv).
Not all radiations have the same biological effect, even for the same amount of absorbed dose.
Equivalent dose is calculated by multiplying absorbed dose (Gy) by a quality factor (QF) that is unique to the type of incident radiation. Quality factors (QF) for some radiations are:
• Gamma and X rays: 1
• Beta particles: 1
• Alpha particles: 20
• Thermal neutrons (lower energy): 2
• Fast neutrons (higher energy): 10
• Protons: 10
• Heavy ions: 20
Roentgen (R): The roentgen is a unit used to measure a quantity called "exposure". This unit is used only for gamma and X rays with energy less then 3.5 MeV, and only applies in air. One roentgen is equivalent to depositing 2.58 x 10-4 coulombs per kg of dry air. It is a measure of the ionizations of molecules in a mass of air. The main advantage of the Roentgen is that it is easily measured directly.
1.2.3. Radiation dose rate in the vicinity of a point source of gamma rays
There is an empirical relation between the radiation dose rate in air (exposure in R/h) and the activity A (Ci) of a point source of gamma rays in a distance r (m):
P = Γ . A/r2
where: dose rate factor Γ is an empirical factor for the specific radioisotope that includes absorption, geometry, photon per disintegration, energy, and all other factors that affect the dose rate from the radioisotope at unit distance. The inverse-square law of gamma absorption in air is assumed as long as the source can be considered a point source. The absorption of gamma rays in air is also assumed to be negligible. Dose rate factors are given in R/h for 1 Ci at 1 m. Γ factors are usually
60
1.35, 137Cs of 0.30, and 198Au of 0.23. This empirical relation is used in field radiotracer work as a simple approach for rough calibration of radiation detectors.
1.3. RADIATION DETECTION
Since radiation cannot be detected with normal senses, special instruments are designed to indicate the presence of ionizing radiations. The phosphorescent screen where Roentgen observed X ray was the first real-time detector and the precursor to the scintillation crystal detectors still in use today.
The gas filled radiation detector was discovered by Hans Geiger while working with Ernest Rutherford in 1908. The design of this device was later refined by Hans Geiger and W. Mueller, in the 1920s. It is sometimes called simply a Geiger counter or a G-M counter and is commonly used in portable radiation detection instruments.
The function of a radiation detector is to convert radiation energy into an electrical signal. There are two basic mechanisms for converting this energy: excitation and ionization. In ionization, an electron is stripped from an atom, and electron and resulting ion are electrically charged. These charged particles can be influenced by an electric field to induce a current that can be measured directly or converted into a voltage pulse. Ionization chambers, Geiger Mueller tubes, BF3 or 3He neutron detectors, and other gas proportional detectors are examples of ionization detectors.
In excitation, electrons are excited to a higher energy level and when the vacant electron is filled, electromagnetic radiation is emitted. Scintillation detectors such as NaI, BGO, CsI, Polyvinyl toluene (PVT) plastic scintillator and neutron sensitive glass fibers are examples of scintillation detectors. Scintillation crystals respond to radiation by emitting a flash of light proportional to the energy of the photon that is stopped in the crystal. Photomultiplier tubes are used to convert the light emitted by these detectors into electrical pulses which can then be processed.
The most recent class of detector developed are semiconductor (or solid state) detectors. These detectors convert the incident photons directly into electrical pulses. Solid state detectors are fabricated from a variety of materials including: germanium, silicon, cadmium telluride, mercuric iodide, and cadmium zinc telluride. Choice of detector for a given application depends on several factors. For instance, germanium detectors have the best resolution, but require liquid nitrogen cooling which makes them impractical for portable applications. Silicon, on the other hand, needs no cooling, but is inefficient in detecting photons with energies greater than a few tens of keV. In the last few years detectors fabricated from high Z semiconductor materials have gained acceptance due to their ability to operate at room temperature and their inherent high efficiency. Detectors made from cadmium telluride and cadmium zinc telluride are routinely used.
1.3.1. Gas filled radiation detectors
The most common type of instrument is a gas filled radiation detector. Ionization chamber, gas proportional and Geiger Muller detectors for alpha, beta and gamma rays, as well as BF3 and He-3 gas proportional detectors for neutrons are examples of gas filled detectors. These detectors work on the principle that as radiation passes through air or a specific gas, ionization of the molecules in the air occurs (Fig.8).
FIG. 8. Gas filled detector and its response curve
When a high voltage is placed between two areas of the gas filled space, the positive ions will be attracted to the negative side of the detector (the cathode) and the free electrons will travel to the positive side (the anode). By placing a very sensitive current measuring device between the wires from the cathode and anode, the small current measured and displayed as a signal. The amplitude of the output pulse depends on the applied voltage between the cathode and the anode. The more radiation which enters the chamber, the more current displayed by the instrument.
1.3.2. Scintillation radiation detectors
The second most common type of radiation detecting instrument is the scintillation detector. A scintillator is a material that converts energy lost by ionizing radiation into pulses of light. Sodium iodide, NaI (Tl), cesium iodide, CsI, and bismuth germanate, BGO are all examples of scintillation detectors. The commonly used in field radiotracer applications is the NaI(Tl).
The scintillation detector system consists of a scintillator coupled optically to a photomultiplier tube (PMT), which is connected through certain amplifiers to either pulse-height analyzers, or to scalers and ratemeters. The light produced from the scintillation process is converted into light (photons) by so-called photoeffect process. The photoelectrons are then accelerated by an electric field applied inside the PMT, where a multiplication process takes place. The result is that each light pulse (scintillation) produces a charge pulse on the anode of the PMT that can subsequently be detected by other electronic equipment, analyzed or counted with a scaler or a ratemeter.
Scintillation detector may be used as a proportional spectrometer by analyzing the pulse-height distribution. Since the intensity of the light pulse emitted by a scintillator is proportional to the energy of the absorbed gamma radiation, the latter can be determined by measuring the pulse height spectrum.
This is called gamma spectroscopy. Both methods, gamma total and gamma spectrometric measurements are employed in radiotracer applications.
1.3.3. Semiconductor (solid state) detectors
The most recent class of detectors developed are the semiconductor (or solid state) detector, which work on the principle that they collect the charge generated by ionizing radiation in a solid.
These detectors are made of semi-conducting material and are operated much like a solid state diode with a reverse bias. The applied high voltage generates a thick “depletion layer” and any charge created by the radiation in this layer is collected at an electrode. The charge collected is proportional to the energy deposited in the detector and therefore these devices can also yield information about the energy of individual particles or photons of radiation. These detectors convert the incident photons
FIG. 9. Principle of semiconductor (solid state) detector
Solid state detectors are fabricated from a variety of materials including: germanium, silicon, cadmium telluride, mercuric iodide, and cadmium zinc telluride. The best detector for a given application depends on several factors. For instance, germanium detectors have the best resolution, but require liquid nitrogen cooling which makes them impractical for portable applications. Silicon, on the other hand, needs no cooling, but is inefficient in detecting photons with energies greater than a few tens of keV (kilo electron volts). In the last few years detectors fabricated from high Z semiconductor materials have gained acceptance due to their ability to operate at room temperature and their inherent high efficiency. Detectors made from cadmium telluride, mercuric iodide, and cadmium zinc telluride are routinely used.
1.3.4. Detector efficiency
More than any other part of the detection system the detector itself determines the overall response function and therefore the sensitivity and minimum detectable count rate of the system. For any detector, there are two important parameters that affect the overall efficiency of the system, geometric efficiency and intrinsic efficiency. By multiplying these values, one can calculate the total efficiency:
• Total efficiency = Geometric efficiency x Intrinsic efficiency
• Counts/Emitted radiations = (Incident /Emitted) x (Counts/Incident) radiations
In radiation measurements, the geometric efficiency is the ratio of the number of radiation particles or photons that hit the detector divided by the total number of radiation particles or photons emitted from the source in all directions. Geometric efficiency is the solid angle subtended by the detector’s active area divided by the area of a sphere whose radius is the distance from the radiation source to the detector. For example, if 10000 gamma rays are emitted from a source and 100 hit the detector then the geometric efficiency εg is 1%.
The geometric efficiency follows a 1/r2 relationship and it drops rapidly as distance increases.
For every doubling of the distance, the geometric efficiency decreases by a factor of 4. For example, for a NaI(Tl) 3"x3" detector, the geometric efficiency of 1% would be reached at about 20 cm from the source.
The intrinsic efficiency is the ratio of counts detected to the number of photons or particles incident on the detector and is a measure of how many photons or particles result in a gross count. The intrinsic efficiency of various detectors may range from 100% to very small values such as 0.01%, but are typically around 10 to 50%.
The product of these two efficiencies is the total efficiency, or the number of counts detected, relative to the total number of radiations emitted from the source. As a result, the actual count measured by the system is a fraction of the radiation emitted in the direction of the detector.
Efficiency of radiation detection is expressed in counts per second per specific activity unit (counts x s-1 x Bq-1 x m3, or: cps/μCi/m3). Scintillation detectors NaI(Tl) are commonly used for industrial tracer applications because of their high efficiency for gamma ray detection. The intrinsic efficiency of a 1”x1” NaI(Tl) crystal size detector for 100 keV, 500 keV and 1 MeV energy photon is about 39%, 26%, 10% respectively. For NaI (Tl) 2”x2”, which are commonly used in field tests, the intrinsic efficiency is almost four times higher than for 1”x1”.
1.4. RADIATION PROTECTION AND SAFETY 1.4.1. ALARA principle
Radiotracers emit ionizing radiations, which are potentially hazardous to health and therefore radiation protection measures are necessary throughout all stages of operations. The dose rate at a point is inversely proportional to the square of the distance between the source and the point.
Therefore a radiation worker has to maintain maximum possible distance from a radiation source. The dose received is directly proportional to the time spent in handling the source. Thus the time of handling should be as short as possible.
The radiation intensity at a point varies exponentially with the thickness of shielding material.
Thus a radiation worker has to use an optimum thickness of shielding material against the radiating source. The most elementary means of protection is known as "TDS" or "Time, Distance and Shielding."
• Decreasing the time spent around a radiation source decreases the exposure
• Increasing the distance from a source decreases the exposure
• Increasing the thickness of shielding to absorb or reflect the radiation decreases the exposure For exposures from any source, except for therapeutic medical exposure, the doses, the number of people exposed and the likelihood of incurring exposures shall all be kept as low as reasonably achievable (ALARA principle).
1.4.2. Radiation safety considerations in radiotracer applications
All safety measures must be taken to avoid unnecessary exposure to radiation. The following can be used to facilitate planning of an investigation.
• Radioactive tracers can be detected at low concentrations and through relatively thick walls of pipes and vessels.
• Radiation detectors used are highly sensitive, and can detect radioactivity at low concentrations.
• Short half-life tracers can be used.
• Normally the volume of process flows ensures that radiotracer is diluted to an acceptably safe concentration level.
• Handling of radioactive tracers must not pose a risk, nor there environmental hazards involved.
• During transport of radioactivity to the site of investigation, care should be taken that the dose rate on the container not be higher than 2 mSv/h (200 mR/h). If transported by vehicle the radiation dose rate must not be higher than 15 μSv/h (1.5 mR/h) in the cabin.
• ALARA must always be the slogan when planning a radioactive tracer investigation.
The residual radioactive tracer concentration in the end product should be minimal and at an acceptable concentration level, and, if applicable, be permissible concentration in drinking water.
Example: Permissible concentration of 140La in drinking water is 2x10-5μCi/ml set by the International Commission on Radiological Protection (ICRP). For 131I is 2 x 10-6 μCi/ml and is considered safe for consumption by the general public by the ICRP.
Before commencing any radioactive tracer investigation, a complete study must be made wherein the objectives of the investigation are considered. This will allow the investigator to decide upon the methodology as well as the radioactive tracer to use.
The annual dose limit has to be taken into account and no individual should be exposed beyond the prescribed limit. This dose limit is 1 mSv/year for a member of the public and 20 mSv/year for a radiation worker, according to European regulations. An effective national infrastructure is a fundamental requirement for safety and security of sources. Safety Series No. 120, Radiation Protection and the Safety of Radiation Sources, Principle 10 states that: “the government shall establish a legal framework for the regulation of practices and interventions, with a clear allocation of responsibilities, including those of a Regulatory Authority”.
The preamble to the Basic Safety Standards (BSS) defines the elements of a national infrastructure to be: legislation and regulations; a regulatory authority empowered to authorize and inspect regulated activities and to enforce the legislation and regulations; sufficient resources and adequate numbers of trained personnel.
The Regulatory Authority must also be independent of the registrants, licensees and the designers and constructors of the radiation sources used in practices. Hence users of radiotracers, unless the activity is below the exemption level for that radiotracer, should have an authorization from the appropriate regulatory authority.
A useful IAEA publication that should be used in safety assessments for radiation sources is IAEA-TECDOC-1113, Safety Assessment Plans for Authorization and Inspection of Radiation Sources. This publication provides practice-specific checklists with items to be considered during the safety assessments that will be included in authorization applications and during the inspections by the Regulatory Authority.
Safety assessments should be made for each application of the tracer having an activity above the exemption level, since circumstances and the application environment will differ. Each application should consider both occupational and public exposures and ensure that all exposures are as low as reasonably achievable. The level of the assessment should be commensurate with the hazard posed by the radiation source. Hence detailed assessments should not be required where the risk is small, as is the case with many radiotracer experiments.
The procedures for monitoring workers, including the type of dosimeter, should be chosen in consultation with a qualified expert, such as the radiation protection officer, or as specified by the Regulatory Authority. Depending on the situation, both direct reading dosimeters and thermoluminescent dosimeters (TLDs) or film badges may be needed. For non-uniform exposures, it may be necessary to wear additional dosimeters e.g. for the hands or fingers. Dose records should be kept for each application, where possible, and be available to the Regulatory Authority if requested.
2. RADIOACTIVE TRACERS
2.1. TYPES OF TRACERS
A tracer is any substance whose atomic or nuclear, physical, chemical, or biological properties provide for the identification, observation and following of the behavior of various physical, chemical
or biological processes (dispersion, mixing, kinetics and dynamics), which occur either instantaneously or in a given lapse of time (Fig. 10). There are many kinds of tracers. The radioactive tracers are mostly used for online diagnosis of industrial reactors.
FIG. 10. Tracer principle
For conducting a radiotracer investigation, various requirements need to be met before starting the actual test. The most important of all the requirements is the “Radiotracer” itself. It is of fundamental importance that the radiotracer compound should behave in the same way as the material to be traced. Therefore, the selection of an appropriate tracer is crucial to success of a tracer study. For reliable and meaningful results, an industrial radiotracer must meet the basic requirements such as suitable half-life and energy of radiation, physical and chemical stability, easy and unambiguous detection. It is often difficult to meet all the requirements of an ideal tracer and certain compromises have to be made. Even if a radiotracer meets the required criteria, it may not be available to tracer groups in developing countries.
The behavior of tracer under conditions of the system (physical & chemical conditions) is very important. One must know, before injecting a tracer, how it will behave in the system. In certain circumstances, the tracer injected into a system may undergo decomposition, phase change, undesirable absorption and adsorption, chemical interaction with system constituents leading to incorrect results. For example, para-dibromobenzene when used at high temperature is adsorbed on the surfaces or packing inside the reactor vessel and does not follow, faithfully, the organic liquid phase.
While tracing fluid movement in oilfield (inter-well tracing), the reservoir physical and geochemical conditions pose constraints and an undesirable tracer-loss or delay occurs. Sometimes, tracers found to behave properly in one reservoir, may not behave satisfactorily in another reservoir.
While tracing aqueous phase (in a liquid/solid phase system like, waste water treatment plant, oil reservoirs, etc), cationic tracers, with certain exceptions, may lead to problem of sorption and ion exchange with host material.
2.1.1. Intrinsic and extrinsic tracers
Intrinsic (or chemical) tracers are molecules containing an isotope (radioactive or stable) of one of the molecule’s natural elements, which makes the labelled molecule particularly detectable by nuclear or conventional methods in systems where the dynamic characteristics of the non-labelled molecules have to be followed. For example, in the case of water, Tritium (1H 3H16O) measured by nuclear techniques (in practice liquid scintillation counting) is an intrinsic tracer. In this case, the water molecule is traced from the inside, in the intimacy of it nucleus, consequently the water tracer will (in practice) follow all movements and reactions of water itself.
Extrinsic (or physical) tracers are made up of atoms or molecules supposed to share the same dynamic characteristics and, in general, the same mass flow behavior as the investigated medium.
Belonging to this category are all the substances that allow tracing outside the molecular or ionic structure. For example, in case of water, Na131I and 51Cr-EDTA are examples of extrinsic tracers for water.
2.2. ADVANTAGES OF RADIOTRACERS
• Most of the radiotracer applications in industrial reactors make use of artificially produced radionuclides. They have high detection sensitivity for extremely small concentrations, for instance, some radionuclides may be detected in quantities as small as 10-17 grams.
• The amount of radiotracer used is virtually insignificant. For example, 1 Ci of 131I- weighs 8 μg, while 1 Ci of 82Br- weighs only 0.9 μg. That’s why, when injected, they do not disturb the dynamics of the system under investigation.
• They offer possibility of “in-situ” measurements, providing information in the shortest possible time.
• A gamma emitting radiotracer can be measured through radiation transmission, from the outside of a pipe or vessel. This is of special importance for many industrial plant studies.
• Disappearance of the radiotracer from the medium under investigation through radioactive decay provides for a repetition of experiments on the same location with the same tracer, all while pollution declines to a minimum.
• Radioactive tracer can be selective. Several tracers may be employed simultaneously and owing to their characteristic radiation emissions, they can be measured accurately with the help of spectrometry.
One of advantages of radiotracer is based on simple fact that it is easier to detect radioactive than non-radioactive isotopes of the same elements. Vigorous development of analytical technology making possible the attainment of lower and lower detection limits has challenged radioisotope techniques in their most conspicuous stronghold: the limits of detectability.
Advances in the performance of modern instrumental analysis in such branches as gas and liquid chromatography, fluorimetry, atomic emission, and mass spectrometry are reaching ppb levels.
In some applications radiotracers may rank lower (on a comparative basis) than chemical, fluorescent, or stable isotopes regarding some practical aspects. If a non-radioactive tracer can perform the task, it should be preferred. Let’s see some examples.
Example 1: Comparing radiotracer 24Na versus stable isotope 23Na
Chemical behavior of radiotracer 24Na is the same of stable 23Na. Detection limits of conventional analytical techniques for sodium are typically of the order of nanograms, that is (10-9/23) x 6.02 x1023 = 2.6 x1013 atoms. In routine work radiotracer will allow to detect quantities 105 times smaller than conventional techniques.
Example 2: Comparison of tritium measurement techniques
Isotope ratio mass spectrometry (IR-MS) detects tritium at the level of 5 TU = 0.59 Bq/L. Low background liquid scintillation counter (LSC) detects tritium in routine at the level of 1 TU (1 TU equals 1 tritium atom in 1018 hydrogen atoms), so it is clear that LSC is an exceedingly sensitive method.
Example 3: Radiotracer versus rhodamine in water field measurements
Let’s compare radiotracer NH482Br commonly used in wastewater hydrodynamic investigations, with fluorescent dye Rhodamine-WT, which also is used frequently as water tracer. Rhodamine-WT can be measured down to ppb range in portable fluorometers. Activity concentration of 80 mCi (~3GBq) per g of NH482Br is obtained at a low flux reactor at 6.6x1011 n/cm2s. Assuming that 10 g of this irradiated salt suffers a quite high dilution in about 106 m3 of water, resulting mean activity
concentration is about 3x104 Bq/m3 = 30 Bq/L, which can be measured very easy. Rhodamine-WT is sold as a 20% solution. Thus, after it suffered same dilution concentration would be 2 ppb. This is only slightly above detection limit of fluorometers, but many times higher than the concentration required for radiotracer. It is thus evident that radiation detection is a much more sensitive method. However, if one looks at mass of dye, it would correspond to 2 mg/m3 x 106 m3 = 2000000 mg = 2 Kg, that means 10 L, which still is a handy volume to manipulate elsewhere in fieldwork. This explains why rhodamine is becoming competitive as water tracers, especially in rivers and other water basins.
2.3. SELECTION OF A RADIOTRACER
Factors that are important in selection of a radiotracer are given as follows:
• Physical/chemical compatibility with the material to be traced
• Half-life
• Specific activity
• Type and energy of radiation emitted
• Availability and cost
• Method of measurement (sampling or in-situ measurement)
• Handling of radioactive materials, radiological protection/regulations.
Under certain circumstances, tracer has to be chemically identical with the traced substance and then one has to use an intrinsic tracer (also called ‘chemical radiotracer’). This is the case when studying chemical reaction kinetics, solubility, vapour pressures, processes dominated by atomic and molecular diffusion, etc. Radioactive isotopes of the traced elements and labelled molecules are used as intrinsic tracers, for example, 1H3HO for water, 24NaOH for NaOH or 14CO2 for CO2, etc..
Whenever the chemical identity of the tracer with the material it follows is not required, the tracer has merely to fulfill a limited number of not very stringent physical and physiochemical conditions. This type of tracer is commonly referred to as an extrinsic (or physical) radiotracer. The majority of tracer techniques applied in industry make use of these extrinsic radiotracers. When tracing elements or compounds in systems where no chemical changes occur, the radiotracer does not have to be chemically representative of the element or compound. For example, when water in a plant process is being traced, the only requirement of the tracer is that it behaves as the water behaves under the conditions of the plant process.
Some of the many radiotracers that have been successfully used in this case are 198Au as gold chloride (effective tracer 198AuCl4-), 24Na as sodium nitrate (effective tracer 24Na+), 131I as sodium iodide (effective tracer 131I-).
Table I lists some of the commonly used radiotracers in industry.
TABLE I. COMMONLY USED RADIOTRACER IN INDUSTRY Isotope Half-life Radiation and Energy
(MeV)
Chemical Form Tracing of phase Tritium (3H) 12.6 y Beta, 0.018(100%) Tritiated water Aqueous
Sodium-24 15 h Gamma:
1.37(100%) 2.75(100%)
Sodium carbonate Aqueous
Bromine-82 36 h Gamma:
0.55 (70%) 1.32 (27%)
Ammonium bromide, p-dibrom-benzene, Dibrobiphenyl CH3 Br, C2H5Br
Aqueous Organic Organic Gases
Lanthanum-140 40 h Gamma:
1.16 (95%) 0.92 (10%) 0.82(27%) 2.54 (4%)
Lanthanum chloride, Lanthanum oxide
Aqueous/Solids Solids
Gold-198 2.7 d Gamma: 0.41 (99%) Chloroauric acid Aqueous/Solids Mercury-197 2.7 d Gamma: 0.077(19%) Mercury metal Mercury Iodine-131 8.04 d Gamma:
0.36 (80%) 0.64 (9%)
Potassium or Sodium iodide,
Iodobenzene
Aqueous Organic
Chromium-51 28 d Gamma: 0.320 (9.8%) Cr-EDTA, CrCl3 Aqueous Technetium-99m 6 h Gamma: 0.14 (90%) Sodium pertechnetate
(TcO4-)
Aqueous
Scandium-46 84 d Gamma:
0.89(100%) 1.84(100%)
Scandium oxide Scandium chloride ScCl3 (Sc3+)
Solids
Aqueous/Solids
Xenon-133 5.27 d Gamma: 0.08 (100%) Xenon Gases
Krypton-85 10.6 y Gamma: 0.51(0.7% ) Krypton Gases
Krypton-79 35 h Gamma: 0.51 (15%) Krypton Gases
Argon-41 110 min Gamma: 1.29(99% ) Argon Gases
2.4. METHODS AND TECHNIQUES FOR LABELLING 2.4.1. Solid materials
A. Internal (mass) labelling
A common method for labelling of a solid material is direct activation i.e., to irradiate a portion of the traced material in a neutron flux and induce the necessary activities. Table II gives examples of widely used tracers labelled by direct activation of solids. Specially produced glasses containing a chemical element that can be activated by (n, γ) reactions, are available to any given size distribution and are used very extensively as sand tracers. 198Au, 51Cr, 192Ir and 46Sc are the radioactive nuclides often induced.
TABLE II. SOME RADIOACTIVE TRACERS INDUCED BY DIRECT ACTIVATION OF SOLIDS Irradiated material Induced radionuclides
Coal 46Sc, 59Fe
Clinker, cement 24Na, 140La Cracking catalyst 140La
Gold ore 198Au, 59Fe, 42K, 140La, 56Mn, 24Na, 46Sc,51Cr Copper ore 64Cu, 42K, 140La, 24Na, 59Fe
Activity calculation of irradiated target in the nuclear reactor
Two major producers of artificial radioisotopes are nuclear reactors and accelerators.
Radioisotopes produced in nuclear reactors represent a large percentage of the total use of radiotracers due to a number of factors. The nuclear reactor offers relatively large volume for irradiation, simultaneous irradiation of several targets, economy of production and possibility to produce a wide variety of radioisotopes. There are more than 50 reactor-produced radioisotopes, many of them suitable for using as radiotracers. The accelerator-produced isotopes relatively constitute a smaller percentage of total use, mostly in nuclear medicine, in particular for PET (positron emission tomography) diagnosis. The accelerators are generally used to produce those isotopes which can not be produced by nuclear reactors or which have unique properties, such as F-18 and radioisotope generator
88Ge/88Ga.
Radioisotopes are produced by exposing suitable target materials to the neutron flux in a nuclear reactor for an appropriate time. The nuclear reactors mostly used for radioisotope production are with the power of around 1 MW. The 250 kW Triga Mark II reactor, which is in operation in some developing countries, still offers the possibility to activate various substances. Despite the degrees of freedom provided by many reactors it is not always applicable as the reactor time is restricted and neutron flux is too low for some applications.
When a target is under irradiation in a nuclear reactor, the activation per second can be represented by:
dN*/dt = Φ σ NT where:
• Φ is the neutron flux (n/cm2 s)
• σ is the activation section (neutron capture cross-section, 1024 barn)
• N* is the number of activated atoms (atoms/g)
• NT is the total number of atoms present in the target (atoms/g)
Since the product radioisotope starts decaying with its own half-life, once production starts, the net growth rate of active atoms can be written as:
dN*/dt = Φ σ NT - λ N*
where: λ = ln2/T1/2 = 0.693/ T1/2 is the decay constant of the being created radioisotope, and T1/2 is its half-life.
The above equation can be solved to determine the value of radioactive atoms at the end of irradiation time ti, as follows:
N* = σ Φ NT [1- exp(-λ ti)]
If a delay time (cooling time) td applies after end of irradiation before the radiotracer can be used, the activity A of the irradiated sample at the end of the delay time is:
A = σ Φ NT [1 - exp(-λ ti)] [exp(-λ td )]
Example of sample irradiation and activity calculation
Routinely irradiated samples are e.g. KBr-powder to produce 82Br, NaCO3-powder to produce
24Na, argon filled in a 30 ml quartz capsule at a pressure of 10 bars to provide 41Ar, and many others.
Let us assume an experiment using 82Br as a radiotracer in the aqueous phase has to be performed. Normally the target material for production of 82Br is potassium bromide (KBr). What is the needed irradiation time to achieve an amount of activity given a reasonable amount of target material, a relatively standard flux in a nuclear reactor and a desired cooling time for decay of undesired radioisotopes before application?
The production activity is calculated according to the above mentioned formula:
A = σ Φ NT [1- exp(-λ ti)] [exp(–λ td )]
where:
σ = the thermal neutron reaction cross section in barn (1 barn=10-24 cm2) φ = the neutron flux (in neutrons/cm2⋅s)
NT = the number of target atoms in the target used
ti = irradiation time in the nuclear reactor (normally from few minutes to several days)
td = cooling time after reactor irradiation (manipulation in the hot cells for preparing the appropriate radiotracer compound, transport to the experimental site) till injection in the radiotracer test (normally from several hours to few days).
Here, NT may be expressed in terms of the weight of the target compound:
⋅100
⋅
⋅
= ⋅
c
N E A c
T M
I N N
N w
where
• wc = weight of target compound used in g
• NA = Avogadro’s number (= 6.023 x 1023 atoms)
• NE = number of equivalents of the target element in the target compound
• IN = natural abundance of the target nuclide in the target element (in %)
• Mc = molecular weight of the target compound
Combining both above described equations, it gives:
d
i t
t c
N E A
c e e
M
I N N
A w − − ⋅ ⋅ − ⋅
⋅
⋅
⋅
⋅ ⋅
⋅
=
σ φ
(1 λ ) λ100
This formula gives an estimate of the activity of the radiotracer provided that all the other relevant parameters are known.
If the irradiation time in the nuclear reactor is limited then the amount of target material (wc ) has to be calculated (as the unknown parameter) to obtain the optimal activity (A) required for an experiment. The expression for wc becomes:
